Scattering theory for graphs isomorphic to a homogeneous tree at infinity
Mathematical Physics
2013-05-20 v2 math.MP
Spectral Theory
Abstract
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operator on an homogeneous tree. We developp this scattering theory using the classical recipes for Schr\"odinger operators in Euclidian spaces.
Cite
@article{arxiv.1209.1001,
title = {Scattering theory for graphs isomorphic to a homogeneous tree at infinity},
author = {Yves Colin De Verdière and Francoise Truc},
journal= {arXiv preprint arXiv:1209.1001},
year = {2013}
}
Comments
This paper will appear in Journal of Mathematical Physics